Practice questions
88551 published questions with worked solutions.
- If a circle C passing through the point (4, 0) touches the circle x^2 + y^2 + 4x - 6y = 12 externally at the point (1, −1), then...
- If the parabolas y^2 = 4b(x - c) and y^2 = 8ax have a common normal, then which one of the following is a valid choice for the...
- The plane passing through the point (4, −1, 2) and parallel to the lines x+2 3 = y-2 -1 = z+1 2 and x-2 1 = y-3 2 = z-4 3 also...
- Let n ≥ 2 be a natural number and 0 < < 2. Then ( ^n - )^ 1/n ^ n+1 d is equal to: (where C is a constant of integration)
- If the system of equations x + y + z = 5, x + 2y + 3z = 9, x + 3y + αz = β has infinitely many solutions, then β − α equals:
- An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained...
- Let f: R R be a function such that f(x) = x^3 + x^2f'(1) + xf''(2) + f'''(3), x ∈ R. Then f(2) equals:
- The equation of a tangent to the hyperbola 4x^2 - 5y^2 = 20 parallel to the line x − y = 2 is:
- A point P moves on the line 2x − 3y + 4 = 0. If Q(1, 4) and R(3, −2) are fixed points, then the locus of the centroid of ΔPQR is...
- The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is:
- If _ i=1 ^ 20 ( , ^ 20 C_ i-1 , ^ 20 C_i + ^ 20 C_ i-1 )^3 = k 21 , then k is equal to:
- Consider the quadratic equation (c - 5)x^2 - 2cx + (c - 4) = 0, c ≠ 5. Let S be the set of all integral values of c for which one...
- If the area enclosed between the curves y = kx^2 and x = ky^2, (k > 0), is 1 square unit. Then k is:
- Consider a triangular plot ABC with sides AB = 7 m, BC = 5 m and CA = 6 m. A vertical lamp-post at the mid point D of AC subtends...Not in JEE syllabus
- The shortest distance between the point ( 32, 0 ) and the curve y = x, (x > 0), is:
- Let I = _a^b(x^4 - 2x^2) ,dx. If I is minimum then the ordered pair (a, b) is:
- For each t ∈ R, let [t] be the greatest integer less than or equal to t. Then _ x 1^+ (1 - |x| + |1 - x|) ( 2[1 - x] ) |1 - x|...
- If the line 3x + 4y − 24 = 0 intersects the x-axis at the point A and the y-axis at the point B, then the incentre of the...
- The sum of all values of (0, 2 ) satisfying ^22 + ^42 = 34 is:Not in JEE Main syllabus
- Let A be a point on the line r = (1 - 3 ) i + ( - 1) j + (2 + 5 ) k and B(3, 2, 6) be a point in the space. Then the value of μ...